The Frenchman often flattered to deceive in the 2018/19 season, which began with him often being overlooked by previous boss Jose Mourinho.
Speaking in Singapore ahead of United facing Inter Milan, Solskjaer said: "Anthony can be a world class forward.
"I think if you followed Anthony the way he has come back to pre-season, his attitude is spot on.
"I think he has always got the quality and talent, so I expect him, and Marcus (Rashford), to be even better than last season.
"Anthony had a top season when he came, I expect we will see a better Anthony next season."